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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (12): 2321-2329    DOI: 10.3785/j.issn.1008-973X.2022.12.001
    
Time-optimal trajectory planning of manipulator based on multi-group competition squirrel search algorithm
Ye-he ZHAO1,2(),Da-xin LIU1,2,Zhen-yu LIU1,2,*(),Jian-rong TAN1,2
1. State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China
2. Engineering Research Center for Design Engineering and Digital Twin of Zhejiang Province, Hangzhou 310027, China
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Abstract  

Aiming at the problems of low optimization efficiency, poor global and stability of optimization results in the application of traditional intelligent optimization algorithms to time-optimal trajectory planning of manipulator in the joint space, a new time-optimal trajectory planning method for manipulator was proposed. The position constraints were considered when the time-optimal trajectory planning model in the joint space of the manipulator was established. According to the input joint point sequence, an S-shaped curve was used to estimate the time interval, and all the individuals in the algorithm were generated to perform multi-group competition iterations. After that, the time-optimal solution of trajectory planning of manipulator in the joint space was obtained. Results of simulation comparison experiments with different algorithms show that the proposed method has higher optimization efficiency and better global optimization than the traditional optimization algorithms. Also, the proposed method has good stability. The variance of its multiple optimization results can be 3 orders of magnitude lower than that of the single population algorithm.

Key words： joint space      trajectory planning      squirrel search algorithm      polynomial interpolation      manipulator     
Received: 19 January 2022      Published: 03 January 2023
CLC:  TP 242  
Fund:  国家重点研发计划资助项目(2019YFB1312600)；浙江省重点研发计划资助项目(2021C01008)
Corresponding Authors: Zhen-yu LIU     E-mail: zhaoyehe@zju.edu.cn;liuzy@zju.edu.cn
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Ye-he ZHAO
Da-xin LIU
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Cite this article:

Ye-he ZHAO,Da-xin LIU,Zhen-yu LIU,Jian-rong TAN. Time-optimal trajectory planning of manipulator based on multi-group competition squirrel search algorithm. Journal of ZheJiang University (Engineering Science), 2022, 56(12): 2321-2329.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2022.12.001     OR     https://www.zjujournals.com/eng/Y2022/V56/I12/2321


基于多种群竞争松鼠搜索算法的机械臂时间最优轨迹规划

针对传统智能优化算法在机械臂关节空间进行时间最优轨迹规划应用中存在的寻优效率低、优化结果全局性和稳定性差的问题，提出新的机械臂时间最优轨迹规划方法. 在建立机械臂关节空间内的时间最优轨迹规划模型时考虑位置约束，根据输入的关节点列，使用S形曲线估算时间的取值区间，对生成算法的所有个体进行多种群竞争迭代，得出机械臂关节空间轨迹规划的时间最优解. 与不同算法的仿真对比试验结果表明，所提方法较传统的优化算法具有更高的寻优效率和更好的优化全局性；所提方法的稳定性好，其多次优化结果的方差相较单种群算法低3个数量级.


关键词： 关节空间,  轨迹规划,  松鼠搜索算法,  多项式插值,  机械臂 
Fig.1 Flow chart of squirrel search algorithm
Fig.2 Schematic diagram of multi group competition strategy
Fig.3 Flow chart of solving time-optimal trajectory planning problem based on multi-group competition squirrel search algorithm
Fig.4 Picture of robotic arm
i αi?1/（°） ai?1/mm di/mm θi/（°）
1 0 0 249 0
2 90 0 0 0
3 90 0 264 0
4 ?90 0 0 0
5 90 0 243 0
6 ?90 0 0 ?90
7 ?90 90 80 ?90
Tab.1 D-H parameters of robotic arm
Fig.5 Comparison of trajectory optimization results with and without position constraints
点列 I/（°）
关节1 关节2 关节3 关节4 关节5 关节6 关节7
0 0 70 0 70 ?20 ?40 0
1 40 ?5 ?90 60 40 20 60
2 160 65 ?10 20 5 ?60 120
3 50 ?10 ?70 90 ?60 20 ?30
4 ?25 50 ?25 40 150 ?70 60
5 ?120 ?40 ?75 90 ?5 ?130 ?50
Tab.2 Joint position sequence of robotic arm
Fig.6 Fitness curve of squirrel search algorithm
Fig.7 Fitness curve of genetic algorithm
Fig.8 Fitness curve of multi-group competition squirrel search algorithm
Fig.9 Joint trajectory image of  robotic arm
点数 $ {t_{{\text{GA}}}} $/s ${t_{{\text{SSA}}}}$/s ${t_{{\text{MSSA}}}}$/s ${I_{{\text{SSA}}}}$/% ${I_{{\text{MSSA}}}}$/%
7 13.432 6 12.569 5 12.522 8 6.425 4 6.773 1
8 15.252 4 13.771 7 13.646 7 9.708 0 10.527 5
9 16.566 1 15.763 8 15.049 4 4.843 0 9.155 4
10 18.014 9 16.847 9 16.171 5 6.478 0 10.232 6
11 19.629 1 17.713 9 17.505 1 9.756 9 10.820 7
12 21.862 3 19.590 9 18.928 4 10.389 6 13.419 9
13 23.129 3 20.932 9 19.766 9 9.496 2 14.537 4
14 24.193 2 22.209 0 21.256 7 8.201 5 12.137 7
15 26.475 5 23.676 0 22.580 1 10.573 9 14.713 2
16 30.319 4 27.810 1 25.683 9 8.276 2 15.288 9
17 33.922 3 30.674 3 29.208 6 9.574 8 13.895 6
18 34.506 4 31.016 3 30.525 7 10.114 4 11.536 1
19 36.061 2 33.230 9 32.802 3 7.848 6 9.037 1
20 39.790 4 36.577 9 34.787 0 8.073 6 12.574 4
Tab.3 Comparison of interpolation time calculated by various algorithms under different number of path points
算法 $\overline T$/s ${S^2}$/s2
GA 11.671 2 0.019 6
SSA 11.119 6 0.018 0
MSSA 11.049 4 8.5×10?5
Tab.4 Stability comparison of algorithm optimization results
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